Electron-positron Correlation Effects Research Articles

Enhancement of positron binding energy in molecules containing π bonds

Observation of vibrational Feshbach resonances in the annihilation spectra of positrons on molecules provides a direct measurement of the positron-molecule binding energy ${\ensuremath{\varepsilon}}_{B}$. Annihilation measurements are presented for ring hydrocarbons with different numbers of $\ensuremath{\pi}$ bonds, for which it is observed that the presence of $\ensuremath{\pi}$ bonds generally increases the positron binding energies. These molecules were chosen because other global molecular parameters (e.g., polarizability, dipole moment, and geometry) are approximately constant, so the observed differences in ${\ensuremath{\varepsilon}}_{B}$ can be related to changes in the nature of the bonds. The molecular ionization potential ${E}_{\mathrm{i}}$ is an exception: for these molecules, the inclusion of $\ensuremath{\pi}$ bonds tends to decrease ${E}_{\mathrm{i}}$, and the number of $\ensuremath{\pi}$ bonds also exhibits a correlation with ${\ensuremath{\varepsilon}}_{B}$. Comparison with other molecules with $\ensuremath{\pi}$ bonds indicates that the changes in ${\ensuremath{\varepsilon}}_{B}$ are better correlated with the changing electronic structure of the bonds rather than with a direct dependence of ${\ensuremath{\varepsilon}}_{B}$ on ${E}_{\mathrm{i}}$. The relationship between the dependence of ${\ensuremath{\varepsilon}}_{B}$ on the number of $\ensuremath{\pi}$ bonds and electron-positron correlation effects (such as virtual positronium formation) is discussed.

Application of the weighted-density approximation to the accurate description of electron-positron correlation effects in materials

We discuss positron-annihilation lifetimes for a set of illustrative bulk materials within the framework of the weighted-density approximation (WDA). The WDA can correctly describe electron-positron correlations in strongly inhomogeneous systems, such as surfaces, where the applicability of (semi-)local approximations is limited. We analyze the WDA in detail and show that the electrons which cannot screen external charges efficiently, such as the core electrons, cannot be treated accurately via the pair correlation of the homogeneous electron gas. We discuss how this problem can be addressed by reducing the screening in the homogeneous electron gas by adding terms depending on the gradient of the electron density. Further improvements are obtained when core electrons are treated within the LDA and the valence electron using the WDA. Finally, we discuss a semiempirical WDA-based approach in which a sum rule is imposed to reproduce the experimental lifetimes.

Quantum Monte Carlo Study of a Positron in an Electron Gas

Quantum Monte Carlo calculations of the relaxation energy, pair-correlation function, and annihilating-pair momentum density are presented for a positron immersed in a homogeneous electron gas. We find smaller relaxation energies and contact pair-correlation functions in the important low-density regime than predicted by earlier studies. Our annihilating-pair momentum densities have almost zero weight above the Fermi momentum due to the cancellation of electron-electron and electron-positron correlation effects.

First-principles method for impurities in quantum fluids: Positron in an electron gas

Calculations of the relaxation energy, contact pair-correlation function, and annihilating-pair momentum density for a single positron immersed in a homogeneous electron gas are presented. We achieve an accurate description of the electron-positron correlation effects by working in the reference frame in which the positron is stationary and using a mean-field approach based on single-component density functional theory. Our positron relaxation energies and annihilation rates are similar to those from the best existing many-body calculations. Our annihilating-pair momentum densities are significantly different from previous data, and include a "tail" beyond the Fermi edge.

Non-Local Electron-Positron Enhancement Factors in Solids

Non-local electron—positron correlation effects in solids are studied. The weighted density approximation is applied to calculations of the non-local electron—positron correlation functions. The calculated weighted density approximation electron—positron enhancement factors for the core electrons are compared with those obtained within the local density approximation. Also, differences in the electron—positron enhancement factors due to the s, p, d and f angular momentum channels of the electron charge density are studied. The formalism is applied to ab initio calculations of positron lifetimes in a variety of metals and silicon. The influence of various approximations to the electron—positron interaction on the positron lifetimes is also presented. The weighted density approximation results are compared to those calculated within the local density approximation, the recent generalized gradient approximation and with experimental data.

First-Principles Calculations of Positron Annihilation in Solids

ABSTRACTWe present first-principles approaches based on density functional theory for calculating positron states and annihilation characteristics in condensed matter. The treatment of the electron-positron correlation effects (the enhancement of the electron density at the positron with respect to mean-field density) is shown to play a crucial role when calculating the annihilation rates. A generalized gradient approximation (GGA) takes the strong inhomogeneities of the electron density in the ion core region into account and reproduces well the experimental total annihilation rates (inverses of the positron lifetimes) by suppressing the rates given by a local density approximation (LDA). The GGA combined with an electron-state-dependent enhancement scheme gives a good description for the momentum distributions of the annihilating positron-electron pairs reproducing accurately the trends observed in the angular correlation (ACAR) or Doppler broadening measurements of the annihilation radiation. The combination of the present positron lifetime and momentum density calculations with the corresponding measurements yields a unique tool for defect identification. Especially, the investigation of various vacancy-type defects in semiconductors able to trap positrons will be an important field for these methods. We will show that the identification of vacancy-impurity complexes in highly n-Type Si and the study of the SiO2/Si interface are particularly interesting applications.

Nonlocal electron-positron correlations in solids within the weighted density approximation

Nonlocal electron-positron correlation effects in solids are studied. The weighted density approximation (WDA) is applied to calculations of the nonlocal state-selective electron-positron correlation functions. The importance of state selectivity of the electron-positron enhancement factors is discussed. The calculated WDA electron-positron enhancement factors for the core electrons are compared with those obtained within the local-density approximation. Also, differences in the electron-positron enhancement factors due to the $s,$ $p,$ $d,$ and $f$ angular momentum channels of the electron charge density are studied. The influence of the electron-positron interaction on the positron density distribution in solids is discussed. The formalism is applied to ab initio calculations of positron lifetimes in a variety of metals and silicon. The influence of various approximations to the electron-positron interaction on the positron lifetimes is also presented. Moreover, we study how the core electrons as well as different angular momentum channels of the valence electron density contribute to the total positron annihilation rates and lifetimes. The results are compared to those calculated within the local-density approximation and the generalized gradient approximation.

Theoretical and experimental study of positron annihilation with core electrons in solids.

A theory for calculating the momentum distribution of annihilating positron-electron pairs in solids is presented. To test the theory, momentum distributions are measured by the Doppler broadening of the annihilation radiation for several bulk metals and semiconductors, as well as for semiconductor alloys and for positrons trapped at vacancies in semiconductors. The theory is based on a two-particle description of the annihilating electron-positron pair. Then, the electron-positron correlation effects, i.e., the enhancement of the electron density at the positron, depend on the electronic state in question. The theory is suited for calculating the high-momentum part of the annihilation spectrum that arises from the core electrons and which can be measured by the Doppler broadening using coincidence techniques. The ideas of the theory are justified by a good agreement between theory and experiment in the case of positron annihilation in undefected bulk lattices. Moreover, the comparison of the theoretical and experimental spectra for alloys and vacancy defects tests the theoretical description for the positron distribution in delocalized and localized states, respectively. @S01631829~96!04327-5#

Electron-positron momentum density in diamond, Si, and Ge.

The electron-positron momentum densities in diamond, Si, and Ge are calculated using a first-principles method. Comparison of the theoretical momentum densities with the experiment shows that the electron-positron correlation effects are very important in Si and Ge, while this effect is negligible in diamond because the electrons are tightly bound. Our analysis shows that only the upper two bands, which consist of the ${\mathit{sp}}^{3}$ hybridized orbitals, contribute to the structures at the low-momentum region of the momentum density. Diamond does not show these structures at the low-momentum region is due to its smaller lattice constant and weak electron-positron correlation effects. \textcopyright{} 1996 The American Physical Society.

Electronic Structure Seen by Positrons in Extended and Reduced Zone Schemes

The influence of the positron on the momentum distribution of annihilation quanta is investigated. Basing on general considerations, we show that a noninteracting positron, which generally reduces electronic densities, may enlarge some particular electronic umklapp components. Numerical tests were performed for alkalis, Al, Cu and Pd by applying augmented plane wave band structure calculations. In the paper we discuss also the influence of this effect on the electron-positron densities after including the electron-positron correlation effects. PACS numbers: 71.25.Pi, 71.60.+z, z, 78.70.Bj

Positron annihilation in II-VI compound semiconductors: theory

Positron states and annihilation rates are calculated for nine different II-VI compound semiconductors. Positron annihilation from the delocalized states in the perfect lattice as well as from the localized states at vacancies and divacancies is considered. The calculations are based on the local-density approximation (LDA) for the electron-positron correlation effects. The calculations are performed using non-self-consistent electron densities and electrostatic potentials obtained by atomic superposition and solving for the three-dimensional positron wavefunctions by a relaxation method. For the perfect lattices, also self-consistent electron densities and positron states (linear muffin-tin orbital method within atomic-spheres approximation, LMTO-ASA) are calculated. The results show that positron annihilation with the outer d electrons of the group II metal atoms plays an important role. The positron lifetimes calculated for perfect lattices are a few per cent shorter than the experimental ones, indicating an LDA overestimation of the d-electron enhancement around the positron. These bulk lifetimes can be corrected efficiently by a semiempirical model introduced in this work. In the case of positrons trapped by defects, the present theoretical description is less satisfactory, because atomic relaxations due neither to rearrangements in the electronic structure nor to the localized positron are taken into account. However, the calculated annihilation probabilities with core and valence electrons will serve as an important database for methods in which defects can be identified using the positron angular correlation or Doppler broadening measurements.

Angular-correlation distribution of positron-electron annihilation in GaAs.

Angular correlation of positron annihilation radiations has been measured along the [100], [110], [111], [211], and [221] crystallographic axes in GaAs using the long-slit geometry. A pseudopotential calculation is carried out to understand the experimental data. There is good agreement between experimental and theoretical data. The structures seen in the low-momentum region of the data are interpreted in terms of the \ensuremath{\sigma} and \ensuremath{\pi} bonds of the ${\mathit{sp}}^{3}$ hybridized bonding orbitals. The experimental data when compared with the calculated data reveal the presence of electron-positron many-body correlation effects.

The electronic structure of alkali metals: experiment and theory

The high-momentum components of the electron and positron Bloch waves in the three alkali metals Li, Na, and K have been studied by comparing calculations employing the linear muffin tin orbital method and the independent particle model with accurate measurements of the two-dimensional angular correlation of annihilation radiation. It is found that such an analysis provides a sensitive test of electronic structure, and that electron-positron correlation effects do not distort the high-momentum components in this example in any significant way. It is shown that thermal effects due to Debye-Waller damping are important.

Interpretation of positron-annihilation data with respect to the electron-positron enhancement factors. II. Applications.

The theoretical considerations of the properties of positron-annihilation characteristics in simple metals, presented in the previous paper, are verified for the alkali metals and Mg. Results are based on a local-density approach to electron-positron correlations and band-structure calculations are performed within the linear-muffin-tin-orbitals--average-spheres approximation. The validity of the average electron density approximation is discussed and the effective densities, determined by electron-positron correlation effects, are presented for valence electrons in simple metals. Methods of extracting the full shape of the electron-positron momentum density from experimental curves are recommended. The proposed analysis of experimental data applied to simple metals allows more reliable verificaton of the shape of electron-positron enhancement factors near the Fermi surface.

Calculation of positron lifetimes in bulk materials

The authors have calculated positron lifetimes in different bulk materials using the LMTO (linear muffin-tin orbitals) method. Electron-positron correlation effects have been included in the calculation through the enhancement factor calculated within the local density approximation (LDA) by Jarlborg and Singh (1989). Following Jensen and Puska (1987), they apply the enhancement factor identically to all electrons (valence and core), making the approach very general. The overall agreement between the calculated bulk lifetimes and the corresponding experimental values is especially good in the case of 3d transition metals. These calculations constitute a good test for the application of the method to angular correlation data analysis.

Electronic structure and electron-positron correlation effects in Mg

A reconstruction of 3D electron-positron densities from 2D ACPAR experimental spectra for Mg was performed using Cormack's method and compared with theoretical results. In theoretical calculations the LMTO band structure method was applied. Many-body effects have been incorporated in a local density approximation both for valence and core electrons. These results lead to improved agreement between theory and experiment in comparison to the independent particle model. For the first time an over-enhancement of the higher momentum components was obtained both theoretically and experimentally.

Electron momentum distribution and spin density of ferromagnetic iron studied by spin-polarised positron annihilation

The authors report the first study of the Fermi surface topology, electron momentum density and spin momentum density in ferromagnetic iron using two-dimensional angular correlation of polarised positron annihilation radiation. A calculation made in the independent-particle model was obtained from the self-consistent linear muffin-tin orbital method. Comparison between experiment and calculation reveals marked discrepancies which are due to both electron-electron and electron-positron correlation effects. Analysis of experimental distributions shows that the large N-centred hole pocket of minority third band does not exist in contrast with the self-consistent calculation results. A parametrised band-structure calculation has been performed to account for the electron-electron correlation effects. Distributions resulting from this procedure were in better agreement with experiment than the self-consistent ones. Once again the nature of electron-positron correlation effects is found to resemble those observed by Sing et al. for nickel. This confirms the systematic trends of electron-positron correlation effects for localised d electrons. The correct description of the relative spin momentum density distribution requires different enhancement factors for majority and minority electron bands.

Positron Annihilation in Ni3Ga

After confirming by magnetization measurements that a Ni 3 Ga single crystal is purely paramagnetic, the two dimensional electron-positron momentum density is measured and subsequently the LCW folded density is constructed. A comparison of the experimental results with complementary independent particle model calculations by APW method leads to a qualitative discussion of electron-positron many-body correlation effects in this system in which the character and the density of the valence electrons differ significantly for each cell of the constituent elements.

Density functional theory of bound states of positrons in negative ions

Bound states of a single positron and a negative ion are studied in the self-interaction-corrected local spin density approximation (SIC-LSDA). The calculations do not include electron–electron or electron–positron correlation effects. The results are found to be in good agreement with restricted Hartree–Fock calculations. Implications for future work including correlation effects are discussed.

Angular Correlation of Positron Annihilation Radiation in Chromium and Molybdenum

Angular correlation of positron annihilation radiation in Cr and Mo were measured. Self-consistent band structure calculations for Mo were carried out by the APW method with state-dependent potentials. Theoretical angular correlations for Cr and Mo were also calculated by the APW method. Observed fine structures on the angular correlations and the crystalline anisotropies were well reproduced by the calculations. However, when the theoretical and experimental correlation curves were normalized to an equal area, the theoretical curves were consistently lower in counting rate than the experimental ones in small angle region, and higher in large angle region. This type of discrepancy between the theory and the experiment is the same as we previously found in V and Nb, and is ascribed to the electron-positron correlation effects.